What is adding intervals property?

Category: QuestionsWhat is adding intervals property?
Editor">Editor Staff asked 11 months ago

What is adding intervals property?
(a) \(\int_a^c\)f(x)dx+\(\int_b^c\)f(x)dx = \(\int_a^c\)f(x) dx
(b) \(\int_a^b\)f(x)dx+\(\int_b^a\)f(x)dx = \(\int_a^c\)f(x) dx
(c) \(\int_a^b\)f(x)dx+\(\int_b^c\)f(x)dx = \(\int_a^c\)f(x) dx
(d) \(\int_a^b\)f(x)dx-\(\int_b^c\)f(x)dx = \(\int_a^c\)f(x) dx
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Editor">Editor Staff answered 11 months ago

The correct choice is (c) \int_a^bf(x)dx+\int_b^cf(x)dx = \int_a^cf(x) dx
To explain I would say: The adding intervals property of definite integrals is \int_a^bf(x)dx+\int_b^cf(x)dx.
\int_a^bf(x)dx+\int_b^cf(x)dx = \int_a^cf(x) dx